Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

A simple proof for the existence of Zariski decompositions on surfaces


Author: Thomas Bauer
Journal: J. Algebraic Geom. 18 (2009), 789-793
DOI: https://doi.org/10.1090/S1056-3911-08-00509-2
Published electronically: March 4, 2008
MathSciNet review: 2524598
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Abstract | References | Additional Information

Abstract: In this note we give a quick and simple proof of the existence (and uniqueness) of Zariski decompositions on surfaces. While Zariski's original proof employs a rather sophisticated procedure to construct the negative part of the decomposition, the present approach is based on the idea that the positive part can be constructed from a maximality condition. It may also be useful that this approach yields a practical algorithm for the computation of the positive part.


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Additional Information

Thomas Bauer
Affiliation: Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Hans-Meerwein-Straße, D-35032 Marburg, Germany
Email: tbauer@mathematik.uni-marburg.de

DOI: https://doi.org/10.1090/S1056-3911-08-00509-2
Received by editor(s): August 9, 2007
Received by editor(s) in revised form: November 7, 2007
Published electronically: March 4, 2008
Additional Notes: The author was partially supported by DFG grant BA1559/4-3

American Mathematical Society